Solving One Species Lotka–volterra Equation by the New Iterative Method (NIM)

Abstract

In this paper, we investigate the use of the new iterative method, referred to as the NIM, for solving the one species LotkaVolterra equation. This equation, which describes the dynamics of populations in ecological systems, has been widely studied in the field of mathematical biology. However, finding an analytical solution to this equation can be challenging. To overcome this, we propose using the NIM as an alternative method for solving the equation. To demonstrate the effectiveness of the NIM, we conduct a comparative study between it and other wellestablished techniques such as the differential transformation method (DTM), the variational iteration method (VIM), and the Adomian decomposition method (ADM). Through numerical simulations, we show that the NIM is able to accurately and efficiently solve the one species LotkaVolterra equation, making it a promising tool for researchers in the field of mathematical biology.